Simplify; express your answer in exponential form. Assume $n\neq 0, p\neq 0$. $\dfrac{{(n^{-1}p^{3})^{-5}}}{{n^{-3}p^{4}}}$
To start, try simplifying the numerator and the denominator independently. In the numerator, we can use the distributive property of exponents. ${(n^{-1}p^{3})^{-5} = (n^{-1})^{-5}(p^{3})^{-5}}$ On the left, we have ${n^{-1}}$ to the exponent ${-5}$ . Now ${-1 \times -5 = 5}$ , so ${(n^{-1})^{-5} = n^{5}}$ Apply the ideas above to simplify the equation. $\dfrac{{(n^{-1}p^{3})^{-5}}}{{n^{-3}p^{4}}} = \dfrac{{n^{5}p^{-15}}}{{n^{-3}p^{4}}}$ Break up the equation by variable and simplify. $\dfrac{{n^{5}p^{-15}}}{{n^{-3}p^{4}}} = \dfrac{{n^{5}}}{{n^{-3}}} \cdot \dfrac{{p^{-15}}}{{p^{4}}} = n^{{5} - {(-3)}} \cdot p^{{-15} - {4}} = n^{8}p^{-19}$